Until now, the algebraic structure of left semi-braces is a quite unexplored field. After the seminal papers of Catino, Colazzo and Stefanelli [1]} and Jespers and Van Antwerpen [2]} interesting results on left semi-braces were given in [3]} and in . In the first one, Catino, Cedó and Stefanelli introduced suitable concepts of nilpotency for left cancellative left semi-braces, extending the ones previously given for skew left braces; in the second one, Stefanelli extended the concept of affine structure on a group given by Rump in  for left braces to study left cancellative left semi-braces \((B,+,\circ )\)  having a fixed group \(H\)  as \((B,\circ )\) .
